In practice, workpieces, such as those obtained from sheet metal by forming, for example deep-drawn parts, often have undesired edge portions which have to be removed. Those edge portions, commonly referred to as “sheet skeleton,” are usually separated from the workpiece as waste through the application of a laser to the workpiece, in which the laser is emitted from a laser cutting head. These edge portions are usually conveyed downwardly away from the workpiece. The resulting large contiguous edge portion often can only be removed from the workpiece with difficulty and/or may cause damage to the laser cutting apparatus given their weight. The large size and/or weight of the edge portions also may present problems during the handling of the removed edge portions during disposal or during recycling.